Question

1. Dado as funções f (x) = x

2 +4x −3 e g (x) = −3x +2, calcule:

a) g (g (x))
b) g (f (x))
c) f (g (x))

Answer 1

Resposta:

Explicação passo-a-passo:

f(x) = x² + 4x − 3  

g(x) = −3x + 2

a) g (g (x)) = - 3(-3x + 2) + 2 =

g (g (x)) = 9x - 6 + 2 =

g (g (x)) = 9x - 4

b) g (f (x)) = - 3(x² + 4x - 3) + 2

g (f (x)) = - 3x² - 12x + 9 + 2

g (f (x)) = -3x² - 12x + 11

c) f (g (x)) = (-3x+2)² + 4(-3x+2) - 3

f (g (x)) = (-3x+2).(-3x+2) + 4(-3x+2) - 3

f (g (x)) = 9x² - 6x - 6x + 4 - 12x + 8 - 3

f (g (x)) = 9x² - 12x + 4 - 12x + 5

f (g (x)) = 9x² - 24x + 9